Proposition 2.3.6 
The triples \((\widetilde{M},B,G)\)  and \((N,B,G)\)  are \(\delta \) -regular weak Abelian fibrations.

We give the proof for the triple \((\widetilde{M},B,G)\)  noting that the proof for the triple \((N,B,G)\)  is analogous. Let \(\mathbf {M}\mathbf {M}_{(0,2\theta ,-2)}\) . By Lemma 3.5.1 in [1]}, tensoring a sheaf by a line bundle with the same Fitting support induces an action \(\mathbf {a}_{\mathbf {M}} \colon \mathbf {G}\times _{B} \mathbf {M}\rightarrow \bf M\) , which restricts to an action \(a_{M} \colon G \times _{B} M \rightarrow M\) . The action \(a_M\)  lifts to a unique action \(\widetilde{a}_M \colon G \times _{B} \widetilde{M}\rightarrow \widetilde{M}\)  since the resolution \(\widetilde{M}\rightarrow M\)  is the blowing up of a locus which is invariant under the action of the group scheme. The proof of Lemma 3.5.4 in [1]} can be adapted to our case to show that the action of \(G\)  on \(M, \widetilde{M},\)  and \(N\)  have affine stabilizers. \(\delta \) -regularity follows from the description of the group scheme given in the upcoming Propositions REF , REF , and REF .
